Question

Consider the following quadratic equation. f(x) = 9x^2

Part A: Write a function, g(x), the shifts f(x) down by 3 units.
Part B: Write a function, h(x), that vertically stretches f(x) by 6 units.
Part C: Write a function, m(x), that reflects f(x) about the x-axis.

Answer 1

• 
  `g(x) = 9x^(2) -3`

• 
  `h(x) = 54x^(2)`

• 
  `m(x) = -9x^(2)`

Step-by-step explanation:

`f(x) = a(x-h)^(2) + k`

a:

• Determines direction.
• Negative x reflects over x-axis.
• a < 1 --> vertically shrunk.
• a > 1 --> vertically streched.

h:

• Determines left and right.
• Sign of h flips...
• (x + h) goes left.
• (x - h) goes right.

k:

• Determines up and down.